Multivariable Plant Set Estimation using Multisinusoidal Input Designs

Abstract A frequency domain method is developed for statistical multivariable plant set estimation. The estimation of a plant “set” rather than a point estimate is required to support many methods of modern robust control design. Results for the multivariable case extend earlier results developed for the single-input single-output (SISO) case. The approach here is based on using multisinusoidal input designs, and acquiring multivariable data from a sequence of single-input multiple-output (SIMO) experiments. Estimators of the plant, output noise, and uncertainty are defined by using the Discrete Fourier Transform (DFT), and statistical properties of the estimators are presented. These properties lead to a precise characterization of the plant set to a specified statistical confidence, e.g., (1-α)-100%.

[1]  J. Schoukens,et al.  Crest-factor minimization using nonlinear Chebyshev approximation methods , 1991 .

[2]  Manfred R. Schroeder,et al.  Synthesis of low-peak-factor signals and binary sequences with low autocorrelation (Corresp.) , 1970, IEEE Trans. Inf. Theory.

[3]  David S. Bayard,et al.  Multivariable Frequency Domain Identification via 2-Norm Minimization , 1992, 1992 American Control Conference.

[4]  Yeung Yam,et al.  A criterion for joint optimization of identification and robust control , 1992 .

[5]  D. Bayard,et al.  A Linear Programming Approach to Characterizing Norm Bounded Uncertainty from Experimental Data , 1991, 1991 American Control Conference.

[6]  Michael Athans,et al.  A Frequency-Domain Estimator for Use in Adaptive Control Systems , 1987, 1987 American Control Conference.

[7]  Robert Bitmead,et al.  Adaptive frequency response identification , 1987, 26th IEEE Conference on Decision and Control.

[8]  P.M.J. Van den Hof,et al.  Quantification of model uncertainty from experimental data: a mixed deterministic-probabilistic approach , 1993 .

[9]  David S. Bayard.  Statistical plant set estimation using Schroeder-phased multisinusoidal input design , 1993 .

[10]  Stephen P. Boyd,et al.  Identification of Systems with Parametric and Nonparametric Uncertainty , 1990, 1990 American Control Conference.

[11]  Graham C. Goodwin,et al.  Quantification of Uncertainty in Estimation using an Embedding Principle , 1989, 1989 American Control Conference.

[12]  Guoxiang Gu,et al.  A class of algorithms for identification in H∞ , 1992, Autom..

[13]  V. Kučera,et al.  Discrete Linear Control: The Polynomial Equation Approach , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  Ron J. Patton,et al.  Comparison of test signals for aircraft frequency domain identification , 1990 .

[15]  R. Younce,et al.  Identification with non-parametric uncertainty , 1990, IEEE International Symposium on Circuits and Systems.

[16]  C. E. Rohrs,et al.  Identification with nonparametric uncertainty , 1992 .

[17]  P. V. D. Hof,et al.  Quantification of model uncertainty from data: input design, interpolation, and connection with robust control design specifications , 1992 .

[18]  C. Sanathanan,et al.  Transfer function synthesis as a ratio of two complex polynomials , 1963 .

[19]  A. Helmicki,et al.  Identification in H∞: a robustly convergent, nonlinear algorithm , 1990, 1990 American Control Conference.

[20]  D. S. Bayard,et al.  An algorithm for state-space frequency domain identification without windowing distortions , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.